Solve for $x$ and $y$ by deriving an expression for $y$ from the second equation, and substituting it back into the first equation. $\begin{align*}-8x-4y &= 3 \\ -5x+2y &= 9\end{align*}$
Answer: Begin by moving the $x$ -term in the second equation to the right side of the equation. $2y = 5x+9$ Divide both sides by $2$ to isolate $y$ $y = {\dfrac{5}{2}x + \dfrac{9}{2}}$ Substitute this expression for $y$ in the first equation. $-8x-4({\dfrac{5}{2}x + \dfrac{9}{2}}) = 3$ $-8x - 10x - 18 = 3$ Simplify by combining terms, then solve for $x$ $-18x - 18 = 3$ $-18x = 21$ $x = -\dfrac{7}{6}$ Substitute $-\dfrac{7}{6}$ for $x$ back into the top equation. $-8( -\dfrac{7}{6})-4y = 3$ $\dfrac{28}{3}-4y = 3$ $-4y = -\dfrac{19}{3}$ $y = \dfrac{19}{12}$ The solution is $\enspace x = -\dfrac{7}{6}, \enspace y = \dfrac{19}{12}$.